%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE090+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:52:23 PM UTC 2026
% Result : Theorem 28.66s 9.84s
% Output : CNFRefutation 28.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 85 ( 81 unt; 4 def)
% Number of atoms : 173 ( 88 equ)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 12 ( 8 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 77 !; 2 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(f14,axiom,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain2) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(f21,conjecture,
! [X0,X1] :
( addition(X0,X1) = X1
=> addition(antidomain(X1),antidomain(X0)) = antidomain(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f22,negated_conjecture,
~ ! [X0,X1] :
( addition(X0,X1) = X1
=> addition(antidomain(X1),antidomain(X0)) = antidomain(X0) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
? [X0,X1] :
( addition(X0,X1) = X1
& antidomain(X0) != addition(antidomain(X1),antidomain(X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f24,plain,
( sK1 = addition(sK0,sK1)
& antidomain(sK0) != addition(antidomain(sK1),antidomain(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f23]) ).
fof(f25,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f26,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f28,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f30,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f31,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f32,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f33,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f36,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f37,plain,
! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(cnf_transformation,[],[f14]) ).
fof(f38,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f44,plain,
sK1 = addition(sK0,sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
antidomain(sK0) != addition(antidomain(sK1),antidomain(sK0)),
inference(cnf_transformation,[],[f24]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f25]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f26]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f27]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f28]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f30]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f31]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f33]) ).
tcf(c_60,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f36]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(cnf_transformation,[],[f37]) ).
tcf(c_62,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f38]) ).
tcf(c_66,negated_conjecture,
addition(antidomain(sK1),antidomain(sK0)) != antidomain(sK0),
inference(cnf_transformation,[],[f45]) ).
tcf(c_67,negated_conjecture,
addition(sK0,sK1) = sK1,
inference(cnf_transformation,[],[f44]) ).
tcf(c_83,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_85,negated_conjecture,
addition(antidomain(sK0),antidomain(sK1)) != antidomain(sK0),
inference(theory_normalisation,[status(thm)],[c_66,c_50,c_49]) ).
tcf(c_132,definition,
iPr_def_10 = antidomain(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_133,definition,
iPr_def_11 = antidomain(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_134,definition,
iPr_def_12 = addition(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_135,definition,
iPr_def_13 = addition(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_136,negated_conjecture,
iPr_def_12 != iPr_def_10,
inference(demodulation,[status(thm)],[c_85,c_133,c_132,c_134]) ).
tcf(c_137,negated_conjecture,
iPr_def_13 = sK1,
inference(demodulation,[status(thm)],[c_67,c_135]) ).
tcf(c_223,plain,
antidomain(iPr_def_13) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_133,c_137]) ).
tcf(c_226,plain,
addition(iPr_def_10,antidomain(iPr_def_10)) = one,
inference(superposition,[status(thm)],[c_132,c_83]) ).
tcf(c_227,plain,
addition(iPr_def_11,antidomain(iPr_def_11)) = one,
inference(superposition,[status(thm)],[c_223,c_83]) ).
tcf(c_228,plain,
addition(sK0,iPr_def_13) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_135,c_137]) ).
tcf(c_229,plain,
addition(iPr_def_13,sK0) = iPr_def_13,
inference(demodulation,[status(thm)],[c_228,c_49]) ).
tcf(c_232,plain,
multiplication(iPr_def_11,iPr_def_13) = zero,
inference(superposition,[status(thm)],[c_223,c_60]) ).
tcf(c_233,plain,
antidomain(one) = zero,
inference(superposition,[status(thm)],[c_60,c_54]) ).
tcf(c_234,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = multiplication(iPr_def_11,iPr_def_13),
inference(demodulation,[status(thm)],[c_60,c_232]) ).
tcf(c_237,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_11,iPr_def_13)) = X0,
inference(demodulation,[status(thm)],[c_51,c_232]) ).
tcf(c_238,plain,
multiplication(iPr_def_11,iPr_def_13) = antidomain(one),
inference(light_normalisation,[status(thm)],[c_233,c_232]) ).
tcf(c_239,plain,
addition(multiplication(iPr_def_11,iPr_def_13),antidomain(multiplication(iPr_def_11,iPr_def_13))) = one,
inference(superposition,[status(thm)],[c_238,c_83]) ).
tcf(c_258,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,iPr_def_13),X0) = X0,
inference(superposition,[status(thm)],[c_237,c_49]) ).
tcf(c_262,plain,
antidomain(multiplication(iPr_def_11,iPr_def_13)) = one,
inference(demodulation,[status(thm)],[c_239,c_258]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_298,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_13),multiplication(X0,sK0)) = multiplication(X0,iPr_def_13),
inference(superposition,[status(thm)],[c_229,c_56]) ).
tcf(c_313,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,antidomain(iPr_def_10))) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_226,c_56]) ).
tcf(c_314,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,antidomain(iPr_def_10))) = X0,
inference(light_normalisation,[status(thm)],[c_313,c_54]) ).
tcf(c_331,plain,
! [X0: $i] : addition(antidomain(X0),one) = one,
inference(superposition,[status(thm)],[c_83,c_265]) ).
tcf(c_335,plain,
addition(iPr_def_11,one) = one,
inference(superposition,[status(thm)],[c_227,c_265]) ).
tcf(c_342,plain,
! [X0: $i] : addition(one,antidomain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_331,c_50,c_49]) ).
tcf(c_389,plain,
multiplication(iPr_def_11,sK0) = multiplication(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_298,c_258]) ).
tcf(c_466,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),multiplication(one,X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_335,c_57]) ).
tcf(c_475,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),X0) = X0,
inference(light_normalisation,[status(thm)],[c_466,c_55]) ).
tcf(c_476,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_11,X0)) = X0,
inference(theory_normalisation,[status(thm)],[c_475,c_50,c_49]) ).
tcf(c_494,plain,
addition(antidomain(multiplication(iPr_def_11,iPr_def_13)),antidomain(multiplication(iPr_def_11,antidomain(antidomain(sK0))))) = antidomain(multiplication(iPr_def_11,antidomain(antidomain(sK0)))),
inference(superposition,[status(thm)],[c_389,c_61]) ).
tcf(c_515,plain,
addition(one,antidomain(multiplication(iPr_def_11,antidomain(iPr_def_10)))) = antidomain(multiplication(iPr_def_11,antidomain(iPr_def_10))),
inference(light_normalisation,[status(thm)],[c_494,c_132,c_262]) ).
tcf(c_746,plain,
! [X0: $i,X1: $i] : addition(X0,addition(multiplication(iPr_def_11,X0),X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_476,c_50]) ).
tcf(c_7214,plain,
addition(iPr_def_10,multiplication(iPr_def_11,antidomain(iPr_def_10))) = addition(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_314,c_746]) ).
tcf(c_7333,plain,
addition(iPr_def_10,multiplication(iPr_def_11,antidomain(iPr_def_10))) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_7214,c_134]) ).
tcf(c_38521,plain,
antidomain(multiplication(iPr_def_11,antidomain(iPr_def_10))) = one,
inference(demodulation,[status(thm)],[c_515,c_342]) ).
tcf(c_38585,plain,
multiplication(one,multiplication(iPr_def_11,antidomain(iPr_def_10))) = multiplication(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_38521,c_234]) ).
tcf(c_100816,plain,
multiplication(iPr_def_11,antidomain(iPr_def_10)) = multiplication(iPr_def_11,iPr_def_13),
inference(demodulation,[status(thm)],[c_38585,c_55]) ).
tcf(c_100818,plain,
addition(iPr_def_10,multiplication(iPr_def_11,iPr_def_13)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_7333,c_100816]) ).
tcf(c_100918,plain,
iPr_def_10 = iPr_def_12,
inference(demodulation,[status(thm)],[c_100818,c_237]) ).
tcf(c_100949,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_136,c_100918]) ).
tcf(c_100950,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_100949]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE090+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/5.39 % Computer : n002.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Wed Sep 23 18:56:55 UTC 2026
% 0.16/5.40 % CPUTime :
% 0.16/5.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.45
% 0.16/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.45
% 0.16/5.45 % Detected problem language: tptp
% 0.16/5.46 % Proving...
% 28.66/9.84 % SZS status Started for theBenchmark.p
% 28.66/9.84 % SZS status Theorem for theBenchmark.p
% 28.66/9.84
% 28.66/9.84 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 28.66/9.84
% 28.66/9.84 % ------ iProver source info
% 28.66/9.84
% 28.66/9.84 % git: date: 2026-07-19 20:42:38 +0200
% 28.66/9.84 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 28.66/9.84 % git: non_committed_changes: false
% 28.66/9.84
% 28.66/9.84 % ------ Parsing...
% 28.66/9.84 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 28.66/9.84 %
% 28.66/9.84
% 28.66/9.84 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 28.66/9.84
% 28.66/9.84 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 28.66/9.84 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 28.66/9.84
% 28.66/9.84 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 28.66/9.84 % ------ Proving...
% 28.66/9.84 % ------ Problem Properties
% 28.66/9.84
% 28.66/9.84 %
% 28.66/9.84 % clauses 23
% 28.66/9.84 % conjectures 2
% 28.66/9.84 % EPR 2
% 28.66/9.84 % Horn 23
% 28.66/9.84 % unary 23
% 28.66/9.84 % binary 0
% 28.66/9.84 % lits 23
% 28.66/9.84 % lits eq 23
% 28.66/9.84 % fd_pure 0
% 28.66/9.84 % fd_pseudo 0
% 28.66/9.84 % fd_cond 0
% 28.66/9.84 % fd_pseudo_cond 0
% 28.66/9.84 % AC symbols 1
% 28.66/9.84
% 28.66/9.84 % ------ Schedule UEQ
% 28.66/9.84
% 28.66/9.84 % ------ Option_UEQ Time Limit: 10.
% 28.66/9.84
% 28.66/9.84
% 28.66/9.84 % ------
% 28.66/9.84 % Current options:
% 28.66/9.84 % ------
% 28.66/9.84
% 28.66/9.84
% 28.66/9.84 %
% 28.66/9.84
% 28.66/9.84 % ------ Proving...
% 28.66/9.84 %
% 28.66/9.84
% 28.66/9.84 % SZS status Theorem for theBenchmark.p
% 28.66/9.84
% 28.66/9.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 28.66/9.84
% 28.66/9.84
%------------------------------------------------------------------------------